2002/11/11 by Melvin Hochster, Hochster, Melvin, Craig Huneke +1 · 1 citation
Mathematics · #13D45 (13E05 13H99 13J10) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #math.AC #msc:13D45 #msc:13H99
paper · pdf · doi:10.48550/arxiv.math/0211172
arxiv created 2002/11/11 · openalex publication_date 2002/11/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this paper is to prove a generalization of Faltings' connectedness theorem which asserts that, for a complete local domain R of dimension n, the punctured spectrum of R/I is connected if the ideal I is generated by at most n-2 elements. We replace the condition that R be a domain by the requirement that the canonical module of R be indecomposable. We also study equivalent conditions for the canonical module to be indecomposable; under mild conditions this is equivalent to the S2-ification of the local ring to be local.